[Produit étoile déformé et équivalence de Morita]
Nous exposons un théorème de non-existence concernant la quantification par déformation d'un espace homogène M, induite par un twist de Drinfel'd : nous montrons qu'un fibré en droites équivariant sur M avec une classe de Chern non triviale et un produit étoile symplectique ne peuvent coexister sur une même variété M. Ceci implique, par exemple, qu'il n'y a pas de produit étoile symplectique sur l'espace projectif complexe induit par un twist basé sur , ou sur toute sous-algébre, pour tout .
We present a simple no-go theorem for the existence of a deformation quantization of a homogeneous space M induced by a Drinfel'd twist: we argue that equivariant line bundles on M with non-trivial Chern class and symplectic twist star products cannot both exist on the same manifold M. This implies, for example, that there is no symplectic star product on the projective space induced by a twist based on or any sub-bialgebra, for every .
Accepté le :
Publié le :
Francesco D'Andrea 1 ; Thomas Weber 1
@article{CRMATH_2017__355_11_1178_0,
author = {Francesco D'Andrea and Thomas Weber},
title = {Twist star products and {Morita} equivalence},
journal = {Comptes Rendus. Math\'ematique},
pages = {1178--1184},
publisher = {Elsevier},
volume = {355},
number = {11},
year = {2017},
doi = {10.1016/j.crma.2017.10.012},
language = {en},
}
Francesco D'Andrea; Thomas Weber. Twist star products and Morita equivalence. Comptes Rendus. Mathématique, Volume 355 (2017) no. 11, pp. 1178-1184. doi : 10.1016/j.crma.2017.10.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.10.012/
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